Solve for $x$ : $6\sqrt{x} + 8 = 9\sqrt{x} + 10$
Solution: Subtract $6\sqrt{x}$ from both sides: $(6\sqrt{x} + 8) - 6\sqrt{x} = (9\sqrt{x} + 10) - 6\sqrt{x}$ $8 = 3\sqrt{x} + 10$ Subtract $10$ from both sides: $8 - 10 = (3\sqrt{x} + 10) - 10$ $-2 = 3\sqrt{x}$ Divide both sides by $3$ $\frac{-2}{3} = \frac{3\sqrt{x}}{3}$ Simplify. $-\dfrac{2}{3} = \sqrt{x}$ The principal root of a number cannot be negative. So, there is no solution.